Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.LinkedList;

public class Main{

    /**
     * @param args
     * @throws IOException 
     */
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader( new InputStreamReader( System.in ) );
        
        int n = 2*Integer.parseInt( in.readLine() );
        for( int i=1; i<(int)(Math.round(Math.sqrt(n))); i++){
            int t = (int) Math.floor(Math.sqrt(n-i-i*i));
            if( n-i-i*i == t*t + t ){
                System.out.print("YES");
                System.exit(0);
            }
        }
        
        System.out.print("NO");
        
    }

}